Abstract
Biochemistry has many examples of linear chain polymers, i.e., molecules formed from a sequence of units from a finite set of possibilities; examples include proteins, RNA, single-stranded DNA, and paired DNA. In the field of mass spectrometry, it is useful to consider the idea of weighted alphabets, with a word inheriting weight from its letters. We describe the distribution of the mass of these words in terms of a simple recurrence relation, the general solution to that relation, and a canonical form that explicitly describes both the exponential form of this distribution and its periodic features, thus explaining a wave pattern that has been observed in protein mass databases. Further, we show that a pure exponential term dominates the distribution and that there is exactly one such purely exponential term. Finally, we illustrate the use of this theorem by describing a formula for the integer mass distribution of peptides and we compare our theoretical results with mass distributions of human and yeast peptides.
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Hubler, S.L., Craciun, G. Mass distributions of linear chain polymers. J Math Chem 50, 1458–1483 (2012). https://doi.org/10.1007/s10910-012-9983-z
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DOI: https://doi.org/10.1007/s10910-012-9983-z